Spring With Mass Lab
Purpose: This lab will study which variables affect the period (T) of a vertical spring with mass.
Background: A period (T) is the time required for simple harmonic motion to complete one cycle. Amplitude is object’s the magnitude of max displacement.
Hypothesis: Since the formula for the period (T) of a spring system is T = 2π(m/k)^(1/2), changing the mass of the system will change the period (T) of the spring system. Specifically, increasing the mass will increase the period (T), thus slowing the rate of motion of the mass as it oscillates.
Apparatus:
Spring Kit (k = 15 N/m)
Hanging mass set (1)
Stopwatch (1)
Procedure: Part 1: Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Pull the spring for an amplitude of 2cm. Conduct the procedure starting with a mass of 50g and increasing it by intervals of 5g each trial for five trials. Record the periods for each mass.
Part 2: Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Hang a constant mass and pull the spring for an amplitude of 2cm. Repeat the process but increase the amplitude by an increments of 2cm per trial for five trails. Record the periods for each amplitude.
Data: Table 1
Change in Period Due to Change in Mass
Trial
Mass (g)
Cycles
Time
Period (s/cycle)
1
50
10
5.87
0.59
2
55
10
5.50
0.55
3
60
10
6.32
0.63
4
65
10
7.00
0.70
5
70
10
7.38
0.74
Table 2
Change in Period Due to Change in Amplitude
Trial
Amplitude (cm)
Cycles
Time
Period (s/cycle)
1
2
10
6.20
0.62
2
4
10
5.95
0.60
3
6
10
6.04
0.60
4
8
10
5.96
0.60
5
10
10
n/a
n/a
Analysis
The graphs show that increasing the hanging mass increases the period (Graph 1.0), and changing amplitude does not affect the period (T) because the slope in Graph 2.0 is practically 0.
Also, note that the change in period (T) due to change in mass (Graph 1.0) follows a positive linear correlation. These models agree with the equation T = 2π(m/k)^(1/2) because amplitude is not in the equation, so changing amplitude won’t affect the period (T). On the other hand, mass (m) is included in the equation and according to the equation, increasing (m) increases the period (T) if the other variable, the spring constant (k) is kept the same.
Purpose: This lab will study which variables affect the period (T) of a vertical spring with mass.
Background: A period (T) is the time required for simple harmonic motion to complete one cycle. Amplitude is object’s the magnitude of max displacement.
Hypothesis: Since the formula for the period (T) of a spring system is T = 2π(m/k)^(1/2), changing the mass of the system will change the period (T) of the spring system. Specifically, increasing the mass will increase the period (T), thus slowing the rate of motion of the mass as it oscillates.
Apparatus:
- Spring Kit (k = 15 N/m)
- Hanging mass set (1)
- Stopwatch (1)
Procedure: Part 1: Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Pull the spring for an amplitude of 2cm. Conduct the procedure starting with a mass of 50g and increasing it by intervals of 5g each trial for five trials. Record the periods for each mass.Part 2: Hang the spring from an elevated area and attach the mass to hang at the bottom of the spring. Hang a constant mass and pull the spring for an amplitude of 2cm. Repeat the process but increase the amplitude by an increments of 2cm per trial for five trails. Record the periods for each amplitude.
Data: Table 1
The graphs show that increasing the hanging mass increases the period (Graph 1.0), and changing amplitude does not affect the period (T) because the slope in Graph 2.0 is practically 0.
Also, note that the change in period (T) due to change in mass (Graph 1.0) follows a positive linear correlation. These models agree with the equation T = 2π(m/k)^(1/2) because amplitude is not in the equation, so changing amplitude won’t affect the period (T). On the other hand, mass (m) is included in the equation and according to the equation, increasing (m) increases the period (T) if the other variable, the spring constant (k) is kept the same.